An arbitrary Lagrangian-Eulerian formulation for creeping flows and its application in tectonic models

Abstract

SUMMARY This paper presents and analyses numerical techniques developed to investigate viscoplastic Stokes flows within a model of lithospheric deformation. In particular, the techniques are related to a subduction model of compressional orogens. The driving mechanism in the model corresponds to the near-rigid convergence and subduction of one mantle lithosphere beneath another in plane strain and this boundary condition forces flow in an overlying viscoplastic model crust. The numerical techniques use the arbitrary Eulerian-Lagrangian formulation in which flows with free surfaces and large deformation are computed on an evolving Eulerian finite-element grid that conforms to the material domain. A regridding algorithm allows the associated Lagrangian motion and fields to be followed, and, in addition, coupled back to the Eulerian calculation of the flow. Mass-flux boundary conditions are used so that the effects of erosion and deposition by surface processes, and mass loss by subduction can be included in the model calculation. The evolving model crustal layer is flexurally compensated using a general elastic beam formulation. The applicability of the numerical techniques to problems ranging from accretionary wedges to crustal and lithospheric scale deformation is discussed. Simple flows, a linear viscous subduction model, a whirl flow, and a quasi-convection model are used to show that the mass conservation, regridding and surface tracking errors are small. The broader applicability of the modelling techniques is reviewed.